Abstract
Context-dependent rewriting systems allow a higher degree of concurrency w.r.t. context-independent ones, since rewriting rules which apply in intersecting contexts and rewrite different items may be applied concurrently, while this cannot happen with a context-independent specification of the same rules. Context-dependent systems can also be seen as a natural generalization of read/write systems, where several readers of the same items may proceed in parallel. However, all the partial ordering semantics which have been given in the past apply, as far as we know, to context-independent systems. In this paper, instead, we investigate the possibility of giving a partial ordering semantics to graph grammars, which can be seen as elegant and general context-dependent rewriting systems. We accomplish that by associating a deterministic occurrence Petri net to each graph derivation. From such a net, then, a partial ordering relating the applied productions, and expressing the causal dependencies among them, can be obtained. The set of all such partial orderings is then the semantics of the given grammar. We also compare our approach with the classical one for concurrency in graph grammars, and we show that, given a derivation, they generate the same dependencies, although our approach is more abstract than the classical one.
Research partially supported by the GRAGRA Basic Research Esprit Working Group n.3299 and by Alenia S.p.A.
Preview
Unable to display preview. Download preview PDF.
References
de Bakker J., de Roever W., Rozenberg G., eds., Linear time, branching time and partial orders in logics and models for concurrency, LNCS 354, Springer 1989.
Degano P., De Nicola R., Montanari U., “A Partial Ordering Semantics for CCS”, on TCS 75, pp. 223–262, 1990.
Degano P., Montanari U., “A Model for Distributed Systems Based on Graph Rewritings”, on Journal of ACM, Vol.34, n.2, 1987.
Ehrig H., “Introduction to the Algebraic Theory of Graph Grammars”, on Proc. International Workshop on Graph Grammars, Springer Verlag, LNCS 73, 1978.
Guessarian I., ed., Semantics of Concurrent Processes, Springer 1990, LNCS 469.
Habel A., “Hyperedge Replacement: Grammars and Languages”, Ph.D. thesis, University of Bremen, 1989.
Hoare C.A.R., “Communicating Sequential Processes”, Prentice Hall, 1985.
Mac Lane S., “Categories for the Working Mathematician”, Springer Verlag, 1971.
Milner R., “Communication and Concurrency”, Prentice Hall, 1989.
Montanari U., Rossi F., “True Concurrency in Concurrent Constraint Programming”, on Proc. ILPS91, MIT Press, 1991.
Montanari U., Rossi F., “Graph Rewriting for a Partial Ordering Semantics of Concurrent Constraint Programming”, will appear on Teorethical Computer Science, special issue on graph grammars, Courcelle B. and Rozenberg eds.
Peled D., Pnueli A., “Proving Partial Order Liveness Properties”, on Proc. ICALP90, Springer-Verlag, LNCS 443, 1990.
Plotkin G., “A structural Approach to Operational Semantics”, TR DAIMI FN-19, Aarhus University, CS Department, 1981.
Reisig W., “Petri Nets: An Introduction”, EATCS Monographs on Theoretical Computer Science, Springer Verlag, 1985.
Saraswat V. A., “Concurrent Constraint Programming Languages”, Ph.D. Thesis, Carnegie-Mellon University, 1989. Also 1989 ACM Dissertation Award, MIT Press.
Winskel G., “Event Structures”, on Petri nets: applications and relationships to other models of concurrency, Springer-Verlag, LNCS 255.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Montanari, U., Rossi, F. (1992). Graph grammars as context-dependent rewriting systems: A partial ordering semantics. In: Raoult, J.C. (eds) CAAP '92. CAAP 1992. Lecture Notes in Computer Science, vol 581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55251-0_13
Download citation
DOI: https://doi.org/10.1007/3-540-55251-0_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55251-2
Online ISBN: 978-3-540-46799-1
eBook Packages: Springer Book Archive